Problem: Simplify the following expression: $ a = \dfrac{5z - 1}{z + 4} + \dfrac{-7}{5} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{5}{5}$ $ \dfrac{5z - 1}{z + 4} \times \dfrac{5}{5} = \dfrac{25z - 5}{5z + 20} $ Multiply the second expression by $\dfrac{z + 4}{z + 4}$ $ \dfrac{-7}{5} \times \dfrac{z + 4}{z + 4} = \dfrac{-7z - 28}{5z + 20} $ Therefore $ a = \dfrac{25z - 5}{5z + 20} + \dfrac{-7z - 28}{5z + 20} $ Now the expressions have the same denominator we can simply add the numerators: $a = \dfrac{25z - 5 - 7z - 28}{5z + 20} $ $a = \dfrac{18z - 33}{5z + 20}$